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Question

In a recent election, Ms. Robbins received $$8,000$$ votes cast by independent voters, that is, voters not registered with a specific political party. She also received $$10$$ percent of the votes cast by those voters registered with a political party. If $$N$$ is the total number of votes cast in the election and $$40$$ percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received? 


A
0.06N+3,200
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B
0.1N+7,200
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C
0.4N+7,200
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D
0.1N+8,000
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E
0.06N+8,000
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Solution

The correct option is E $$0.06 N + 8,000$$
$$\Rightarrow$$  Ms. Robbins received $$8,000$$ votes from independent voters.
$$\Rightarrow$$  $$40\%$$ of $$N$$ are independent voters.
$$\therefore$$   $$60\%$$ of $$N$$ are not independent voters. From this group Ms. Robbins received $$10\%$$ votes.
$$\Rightarrow$$  So, Total votes = $$(\dfrac{10}{100}\times \dfrac{60}{100})N+8000 $$

$$\Rightarrow$$  $$Total\,votes=(0.1\times 0.6)N+8000$$

$$\therefore$$    $$Total\,votes=0.06N+8000.$$

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